Hi Guys I am from Illinois where 95% of the homes have basements. It does look like water entered from hydraulic pressure at the cold joint. There are a couple of solutions.

1st look at the drainage around the home if the soil is low at the house add more around the whole foundation.and install extensions on the downspouts to get water away from the foundation.

If that does not do it but I think it will.

2nd call a basement waterproofing company there are a lot of them. They can channel a drain around the whole perimeter on the inside of the home that empties into a sump pit and is then ejected out. They will cement over the drain channel so carpet can be reinstalled.

Good luck,

Steve Reilly
Owl Inspection Services